I was born on the third day of August. This year, as with every year, that fell on August third, yesterday.
I was born, and I did not know this so I had to look it up*, on the first Saturday in August. Which this year falls on August 4th, today.
I was born on the third day after the second full moon after the summer solstice. Which this year falls on August 4th, that's boring, I've already got an August 4th.
I was born on 10 K'ib'. This year that falls on August 21st, and some years (not this year) it falls twice.
I was born on 14 Xul. This year that fell on July 27th.
And, weirdly, as I pick calendars for their disconnection with our own, I'm getting a fair number of August 4ths.
I was born on 16 Dhū al-Qiʿda, which this year falls on October 2nd I'm told. That's more like the variation I was expecting with certain other things.
Which is sort of the point of this. "Falls on" implies a certain randomness because there is a certain randomness. Solar calendars will tend to group things together so sticking with them will never get me far off from August 3rd, but with the right calendar any day could be one's birthday. And with so many calendars already out there, there are several days for which one can make the argument, "It's my birthday."
Today might be one of your birthdays, without you even knowing it.
When were you born? Don't feel restricted to the 6 ways I answered the question for myself above.
I'd actually like to convert to Venusian or Martian dates (solar calendar, nothing complicated) but I have no idea how to do that. It certainly should be possible.
And then there's a question of, there are 12 months in the year, if we're going with day of the month, why not 12 birthdays a year?
* That's true of everything after this point, which given that I'm not going for perfection here means some of these things might be wrong.